Distillation Control Variables

This chapter provides you with a concept drawing of a distillation column with all of the streams labeled. 

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Pressure is often considered the prime distillation control variable, Pressure affects condensation, vaporization, temperatures, compositions, volatilities, and almost any process that takes place in the column. An unsatisfactory pressure control often implies poor column control. Pressure is therefore paired with a manipulated stream that is most effective for providing tight pressure control. When the top product is liquid, this stream is almost always the condensation rate when the top product is vapor, this stream is almost always the top product rate (see Sec. 17.2.). 

Amplitude of controlled variable Output amplitude limits Cross sectional area of valve Cross sectional area of tank Controller output bias Bottoms flow rate Limit on control Controlled variable Concentration of A Discharge coefficient Inlet concentration Limit on control move Specific heat of liquid Integration constant Heat capacity of reactants Valve flow coefficient Distillate flow rate Limit on output Decoupler transfer function Error... 

Distillation columns have four or more closed loops—increasing with the number of product streams and their specifications—all of which interact with each other to some extent. Because of this interaction, there are many possible ways to pair manipulated and controlled variables through controllers and other mathematical functions with widely differing degrees of effectiveness. Columns also differ from each other, so that no single rule of configuring control loops can be apphed successfully to all. The following rules apply to the most common separations. 

Shinskey (1984) has shown that there are 120 ways of connecting the five main parts of measured and controlled variables, in single loops. A variety of control schemes has been devised for distillation column control. Some typical schemes are shown in Figures 5.22a, b, c, d, e (see pp. 234, 235) ancillary control loops and instruments are not shown. 

Example 1.5. For a binary distillation column (see Fig. 1.6), load disturbance variables might include feed flow rate and feed composition. Reflux, steam, cooling water, distillate, and bottoms flow rates might be the manipulated variables. Controlled variables might be distillate product composition, bottoms product composition, column pressure, base liquid level, and reflux drum liquid level. The uncontrolled variables would include the compositions and temperatures on aU the trays. Note that one physical stream may be considered to contain many variables ... 

Another type of nonlinear control can be achieved by using nonlinear transfonnations of the controlled variables. For example, in chemical reactor control the rate of reaction can be controller instead of the temperature. The two are, of course, related through the exponential temperature relationship. In high-purity distillation columns, a transformation of the type shown below can sometimes be useful to "linearize the composition signal and produce improved control while still using a conventional linear controller. 

The classic example of an interacting system is a distillation column in which two compositions or two temperatures are controlled. As shown in Fig. 8.9h, the upper temperature sets reflux and the lower temperature sets heat input. Interaction occurs because both manipulated variables affect both controlled variables. 

Figure 11.3d shows a process where the manipulated variable affects the two controlled variables and in parallel. An important example is in distilla tion column control where reflux flow aSecte both distillate composition and a tray temperature. The process has a parallel structure and this leads to a parallel cascade control system. 

Alatiqi presented (I EC Process Design Dev. 1986, Vol. 25, p. 762) the transfer functions for a 4 X 4 multivariable complex distillation column with sidestream stripper for separating a ternary mixture into three products. There are four controlled variables purities of the three product streams (jCj, x, and Xjij) and a temperature difference AT to rninirnize energy consumptiou There are four manipulated variables reflux R, heat input to the reboiler, heat input to the stripper reboiler Qg, and flow rate of feed to the stripper Lj. The 4x4 matrix of openloop transfer functions relating controlled and manipulated variables is ... 

A distillation column has the following openloop transfer function matrix relating controlled variables (x, and Xg) to manipulated variables (reflux ratio RR and... 

While the reduced SQP algorithm is often suitable for parameter optimization problems, it can become inefficient for optimal control problems with many degrees of freedom (the control variables). Logsdon et al. (1990) noted this property in determining optimal reflux policies for batch distillation columns. Here, the reduced SQP method was quite successful in dealing with DAOP problems with state and control profile constraints. However, the degrees of freedom (for control variables) increase linearly with the number of elements. Consequently, if many elements are required, the effectiveness of the reduced SQP algorithm is reduced. This is due to three effects ... 

In this example, the five manipulated variables are so assigned to the five controlled variables that the heat input at the reboiler and the distillate composition are fixed and therefore the bottoms flow and composition are allowed to change with the variations in feed flow or composition. 

Interaction is unavoidable between the material and energy balances in a distillation column. The severity of this interaction is a function of feed composition, product specification, and the pairing of the selected manipulated and controlled variables. It has been found that the composition controller for the component with the shorter residence time should adjust vapor flow, and the composition controller for the component with the longer residence time should adjust the liquid-to-vapor ratio, because severe interaction is likely to occur when the composition controllers of both products are configured to manipulate the energy balance of the column and thereby "fight" each other. 

One solution to this problem is to employ inferential control, where process measurements that can be obtained more rapidly are used with a mathematical model to infer the value of the controlled variable, as illustrated in Figure 12. For example, if the overhead product stream in a distillation column cannot be analysed on-line, measurement of a selected tray temperature may be used to infer the actual composition. If necessary, the parameters in the model may be updated, if composition measurement become available, as illustrated by the second measuring device in Figure 12 (dashed lines). 

The optimal control of a process can be defined as a control sequence in time, which when applied to the process over a specified control interval, will cause it to operate in some optimal manner. The criterion for optimality is defined in terms of an objective function and constraints and the process is characterised by a dynamic model. The optimality criterion in batch distillation may have a number of forms, maximising a profit function, maximising the amount of product, minimising the batch time, etc. subject to any constraints on the system. The most common constraints in batch distillation are on the amount and on the purity of the product at the end of the process or at some intermediate point in time. The most common control variable of the process is the reflux ratio for a conventional column and reboil ratio for an inverted column and both for an MVC column. 

Thus with given B0m and V, specification of the set of operations decision variables D°m = d°j, i = 1, NTm] (a total of 2 NTm decision variables) and control variables Um = t-, i = 1,NTm for all distillation tasks in operation m, it will be possible to calculate the overall performance measures for the batch (total distillation time, overall separation, products and intermediates amounts, recoveries, energy, etc.)- The same decision variables may be optimised to achieve some overall objective for the operation, (e.g. overall profit) subject to overall constraints (e.g. overall time, energy, etc.). 

The chemical reaction scheme, kinetic data and other input data are given in Table 9.4. There are 2 control variables in each cut. These are the reflux ratio and the duration of the cut. The results of the optimisation are shown in Table 9.5 and Figure 9.14. The distillation column needs to be operated initially at low optimal reflux ratio to remove most of the water. 

In this section we discuss some basic concepts concerning distillation control degrees of freedom, basic manipulated variables, and constraints. 

For example, let us consider a simple distillation column in which we have specifications on both the distillate and bottoms products (v-ahK and x b lk We go through the design procedure to establish the number of trays and the reflux ratio required to make the separation for a given feed composition. This gives us a base case from which to start. Then we establish what disturbances will affect the system and over what ranges they will vary. The most common disturbance, and the one that most affects the column, is a change in feed composition. Next we propose a partial control structure. By partial we mean we must decide what variables will be held constant. We do not have to decide what manipulated variable is paired with what controlled variable. We must fix as many variables as there are degrees of freedom in the system of equations. 

Startup is at initially total reflux, with the reflux value set at an arbitrarily high value, R = Rinit. Once the distillate composition, XO, exceeds the set point composition, XOset, control of reflux ratio is effected by varying the reflux ratio according to the proportional control relationship RC=KC (X0set-X0). The change from initial startup to controlled withdrawal of distillate is effected by means of the logical control variable Flag . 

In the multiloop controller strategy each manipulated variable controls one variable in a feedback proportional integral derivative (PID) control loop. Taking a single-feed, two-product distillation column with a total condenser and a reboiler as an example, a basic list of possible controlled variables includes the distillate and bottoms compositions, the liquid levels in the reflux accumulator and the column bottom, and the column pressure. The main manipulated variables are the reflux, distillate, and bottoms flow rates and the condenser and reboiler heat duties. 

A 100 kmol/h stream containing 50% mole benzene and 40% mole toluene is sent to a 12-stage distillation column on the sixth stage from the top. The column pressure is 100 kPa, with a total condenser and a reboiler. The distillate is the benzene product with a specification of 6.0% mole toluene, and the bottom is the toluene product with a specification of 6.0% mole benzene. These specifications will be met by manipulating the reflux rate and the reboiler heat duty. It is required to determine the best pairing between the manipulated and controlled variables. 

The interaction between the controller loops is evaluated by calculating the change in a controlled variable that results from a change in a manipulated variable. In the preferred pairing, the reflux rate, AT, controls the distillate composition Cp The change in Q caused by a change in AT, is calculated by Equation 15.5. If AA7, = 0.1 kmol/h, then... 

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